The 2D Euler-Poisson System with Spherical Symmetry

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This article concerns the global-in-time existence of smooth solutions with small amplitude to two space dimensional Euler-Poisson system. The main difficulty lies in the slow time decay (1+t)⁻¹ of the linear system. Inspired by Ozawa, Tsutaya, and Tsutsumi's work, we show that such smooth solutions exist for radially symmetric flows.